The Heilbronn Problem is to find the set of points on the edge of a unit-area shape that maximizes the area of the smallest of these thus formed. The construction of one of these objects is the subject of a problem posed by Lemoine whose solution is the Kiepert hyperbola. These objects have two points defined by a certain angle all three of which are named for Brocard. Whether or not three lines in these objects will be concurrent can be determin
The Heilbronn Problem is to find the set of points on the edge of a unit-area shape that maximizes the area of the smallest of these thus formed. The construction of one of these objects is the subject of a problem posed by Lemoine whose solution is the Kiepert hyperbola. These objects have two points defined by a certain angle all three of which are named for Brocard. Whether or not three lines in these objects will be concurrent can be determined using Ceva's theorem. One method of finding the area of these objects uses the semiperimeter and side lengths and is called Hero's formula. For 10 points, name these planar figures, the area of one of which is half its base times its height.
The Heilbronn Problem is to find the set of points on the edge of a unit-area shape that maximizes the area of the smallest of these thus formed.
triangles